How do you factor 4m^3+9m^2-36m-814m3+9m236m81?

1 Answer
Nov 22, 2016

4m^3+9m^2-36m-81 = (m-3)(m+3)(4m+9)4m3+9m236m81=(m3)(m+3)(4m+9)

Explanation:

The difference of squares identity can be written:

a^2-b^2 = (a-b)(a+b)a2b2=(ab)(a+b)

We will use this with a=ma=m and b=3b=3, but first...

Notice that the ratio between the first and second terms is the same as that between the third and fourth terms, so this cubic will factor by grouping:

4m^3+9m^2-36m-81 = (4m^3+9m^2)-(36m+81)4m3+9m236m81=(4m3+9m2)(36m+81)

color(white)(4m^3+9m^2-36m-81) = m^2(4m+9)-9(4m+9)4m3+9m236m81=m2(4m+9)9(4m+9)

color(white)(4m^3+9m^2-36m-81) = (m^2-9)(4m+9)4m3+9m236m81=(m29)(4m+9)

color(white)(4m^3+9m^2-36m-81) = (m^2-3^2)(4m+9)4m3+9m236m81=(m232)(4m+9)

color(white)(4m^3+9m^2-36m-81) = (m-3)(m+3)(4m+9)4m3+9m236m81=(m3)(m+3)(4m+9)